By Claude Daviau, Jacques Bertrand

ISBN-10: 9814740292

ISBN-13: 9789814740296

We expand to gravitation our past examine of a quantum wave for all debris and antiparticles of every iteration (electron + neutrino + u and d quarks for instance). This wave equation is shape invariant less than Cl3*, then relativistic invariant. it truly is gauge invariant less than the gauge workforce of the normal version, with a mass time period: this used to be most unlikely earlier than, and the end result used to be an impossibility to hyperlink gauge interactions and gravitation.

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19). page 31 August 28, 2015 13:33 Limit Theorem for Nonlinear-9586 32 livre_CD_JB The standard model of quantum physics in Cliﬀord Algebra Of course, as we use the space-time of the restricted relativity, with the choice of a + sign for the time, we get δ00 = 1 ; δ11 = δ22 = δ33 = −1 ; δμν = 0 , μ = ν. 40) Among the ten relations in Eq. 43) S μ ν = iψγ γ ψ. And we get: S3 = φσ3 φ. 44) We see immediately that S3 is one of four analog terms Sμ = φσμ φ. 45) We have already encountered S0 , because: S0 = φσ0 φ = φφ = ρeiβ = det(φ).

We review the charge conjugation. 1 With the Dirac matrices An important part of the standard model of quantum physics is the Dirac wave equation. This comes from the fact that electrons, neutrinos and quarks, are quantum objects with spin 1/2. The standard model explains the spin 1/2 as a relativistic consequence of the Dirac wave equation. This equation is intensively studied in this chapter and slightly modiﬁed in the following chapter. The modiﬁed equation shall be generalized in chapter 6 as a wave equation for a pair electron+neutrino.

Therefore the use of σ2 here is necessary. page 28 August 28, 2015 13:33 Limit Theorem for Nonlinear-9586 livre_CD_JB Dirac equation 29 So Eq. 13) is equivalent to: ∇(−iσ2 ξ ∗ ) + iqA(iσ2 ξ ∗ ) + im(iσ2 η ∗ ) = 0. 16) The system composed of Eqs. 13) is consequently equivalent to one matrix 3 equation: ∇(η − iσ2 ξ ∗ ) + iqA(η iσ2 ξ ∗ ) + im(ξ iσ2 η ∗ ) = 0. 17) Now we let φ= √ ξ −η ∗ √ 2(ξ − iσ2 η ∗ ) = 2 1 ∗2 . 19) This gives and also φσ3 = √ 2(ξ iσ2 η ∗ ) ; φσ3 = √ 2(η iσ2 ξ ∗ ). 20) So Eq. 17) which is equivalent to the Dirac equation Eq.

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